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andrezito [222]

2 years ago

11

If you spin a quarter in space what type of 3D figure would you

1 answer:

hammer [34]2 years ago

6 0

D) cone is similar to a quarter circle

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If f(x) = 2(3^x) + 1, what is the value of f(2)?<br> (1) 13<br> (3) 37<br> (2) 19<br> (4) 54

DanielleElmas [232]

54 that’s the answer

6 0

2 years ago

Read 2 more answers

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

Are 25 milligrams lighter or heavier than 25 centigrams

masya89 [10]

Answer:

<em>25 mg. is lighter than 25 cg.</em>

<em />

Step-by-step explanation:

<em>Well,</em>

<em />

<em>The prefix "milli" means thousandth and the prefix "centi" means hundredth. So a milligram will be one-tenth of a centigram.</em>

<em />

<em>10 mg. = 1 cg.</em>

<em>25 mg. = 2.5 cg.</em>

<em />

<em>2.5 cg. < 25 cg.</em>

<em />

<em>25 mg. is lighter than 25 cg.</em>

8 0

3 years ago

Read 2 more answers

The average American spent $8,508 on health care in 2011. The cost of health care is projected to rise about 5.8% per year for t

klio [65]

<h3>The projected amount the average American spent on health care in 2014 is $ 10075.91</h3>

<em><u>Solution:</u></em>

Given that,

The average American spent $8,508 on health care in 2011

The cost of health care is projected to rise about 5.8% per year for the years 2012-2022

<em><u>The increasing function is given as:</u></em>

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate in decimal

t is number of years

From given,

a = 8508

$r = 5.8 \% = \frac{5.8}{100} = 0.058$

t = 2011 to 2014 = 3 years

<em><u>Substituting the values, we get,</u></em>

$y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91$

Thus the projected amount the average American spent on health care in 2014 is $ 10075.91

4 0

3 years ago

Which ordered pairs (x,y) are solutions to the linear equation 2x+3y=6

Nuetrik [128]

Answer:

I think it is 0,2

Step-by-step explanation:

Because you need to substitute the ordered pairs into the linear equation:

so,

2(0)+3(2) = 6

6=6

The two side, so equation are identical, so the correct answer is (0,2).

I hope this helps!

8 0

3 years ago

Read 2 more answers